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A general and consistent integral finite-difference time-domain (FDTD) formulation on cubical grids for modeling of cylindrical antennas with or without dielectric coating is derived. No additional grid points or modifications of the integral paths are necessary. Instead, effective material properties are modified in the FDTD grid. Thus, even for insulated antennas, the simple cubical structure is maintained. Special integral factors are defined on cubical elements, which take into account the behavior of fields in all directions in the neighborhood of the antenna. Applying these factors to the gap region and along the antenna's axis allows a correct modeling of the influence of the antenna's thickness. Furthermore, integral factors derived for the antenna's ends improve the modeling of the antenna's length. The accuracy of the method is confirmed by a systematic comparison with analytical and numerical results.